Question

A thin cylinder of 100 mm internal diameter and 5 mm thickness is subjected to an internal pressure of 10 MPa and a torque of 2000 Nm. Calculate the magnitudes of the principal stresses (in MPa)

• A. 109.8, 45.2
• B. 109.8, 40.2
• C. 109.8, 31
• D. 109.8, 50

Answer 1

The correct option is B 109.8, 40.2

Given :
$D_i$ = 100 mm,
$D_o$ = 110 mm,
D=105 mm

For Thin cylinder

$J=\pi Dt\left(\frac{D^2}{4}\right)=\pi \times 105\times 5\times (52.5{)}^2$

$=4547729m{m}^4=4.547\times {10}^{6}m{m}^4$

${\tau }_{max}=\frac{T\times r_{max}}{J}$

where
$r_{max}=\frac{D_o}{2}=55mm$

$\therefore {\tau }_{max}=\frac{2000\times {10}^3\times 55}{4.547\times {10}^6}=24.20MPa$

${\sigma }_H={\sigma }_c=\frac{p{d}_i}{2t}=100MPa$

${\sigma }_L=50MPa$


${\sigma }_{1^{\prime }}{\sigma }_2=\frac{150}{2}\pm \sqrt{{25}^2+{24.20}^2}$

$=75\pm 34.8=109.8,40.2MPa$